wavefront

pyoof.aperture.wavefront(rho, theta, K_coeff)

Computes the wavefront (aberration) distribution, \(W(x, y)\). It tells how is the error distributed along the primary dish, it is related to the phase error. The wavefront (aberration) distribution is described as a parametrization of the Zernike circle polynomials multiplied by a set of coefficients, \(K_{n\ell}\).

Parameters:

rho : ndarray

Values for the radial component. \(\sqrt{x^2 + y^2} / \varrho_\mathrm{max}\) normalized by its maximum radius.

theta : ndarray

Values for the angular component. \(\vartheta = \mathrm{arctan}( y / x)\).

K_coeff : ndarray

Constants coefficients, \(K_{n\ell}\), for each of them there is only one Zernike circle polynomial, \(U^\ell_n(\varrho, \varphi)\). The coefficients are between \([-2, 2]\).

Returns:

W : ndarray

Wavefront (aberration) distribution, \(W(x, y)\). Zernike circle polynomials already evaluated and multiplied by their coefficients.

Notes

The wavefront (aberration) distribution it strictly related to the Zernike circle polynomials through the expression,

\[W(\varrho, \vartheta) = \sum_{n, \ell}K_{n\ell}U^\ell_n(\varrho, \vartheta).\]